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Positive Solutions of {Delta <em>u</em>}+<em>u</em>^{(<em>n</em>+2)/(<em>n</em>-2)}=0 on Contractible Domains

Positive Solutions of {Delta <em>u</em>}+<em>u</em>^{(<em>n</em>+2)/(<em>n</em>-2)}=0 on Contractible Domains

Year:    1989

Journal of Partial Differential Equations, Vol. 2 (1989), Iss. 4 : pp. 83–88

Abstract

We show that there are bounded contractible domains in R^n, n ≥ 3, on which the Dirichlet problem for the equation Δu +u^{(n+2)/(n-2)} = 0 admit positive solutions. This result, combining with the well-known nonexistence result of Pohozaev, implies that geometry of the domains plays a crucial role in the solvability of the problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1989-JPDE-5845

Journal of Partial Differential Equations, Vol. 2 (1989), Iss. 4 : pp. 83–88

Published online:    1989-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    6

Keywords: